Nonlinear Adaptive Filters for Acoustic Echo Cancellation in Mobile Terminals - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 245

5

0

5

−

− 10

− 15

C

− 20

− 25 B

− 30 A

− 35

0 2000 4000 6000 8000 10000

Sample number

FIGURE 7.9
Adaptation curves for different estimates of the autocorrelation matrix.

It should be noted that a major advantage offered by the algorithm of
Equation 7.49 is the possibility of directly applying it to the SVFs described
in Section 7.2. According to acoustic echo path behavior, a reduction of the
number of channels can be achieved without substantially affecting the gen-
eral performance, as shown in the last set of experiments in this section. It
is also worth noting that similar learning curves have been obtained for AP
algorithms of order L

2.
In the second set of experiments, the performance of the AP algorithms of
order L

>

>

2 has been evaluated. In these experiments, the diagonal realiza-
tion structure of the pure second-order Volterra filter ( M

=

N ) with a mem-
ory of 30 samples is considered. The adaptation algorithms used are those
of Equation 7.49 for L

2 , 3 , 5, and 10. As a reference, the standard NLMS
algorithm has been chosen. The test conditions are the same as those used
for the first set of experiments. The adaptation curves for the AP algorithms
are shown in Figure 7.10 together with the curve for the NLMS algorithm. In
these experiments the adaptation constants

=

µ i are chosen to reach the same
mean-squared error at convergence for all the algorithms. The improvement
obtained in the convergence rate by the AP algorithms is clear. It can also be
noted that even the simple AP algorithm of order 2 is sufficient to guarantee
a convergence rate more than three times higher than that of the NLMS algo-
rithm. Increasing the order of the AP algorithms produces further increments
in the convergence rate. It is worth noting that the better performances of the
AP algorithms with respect to the NLMS algorithm are strictly related to the
correlations existing in the actual and augmented input signals.
Finally, the good tracking characteristics of the AP algorithms can be ap-
preciated from Figure 7.11, where the learning curve of the AP algorithm of
order 2 is shown, together with that for the NLMS algorithm, when a mis-
match affects the echo path. The mismatch was obtained by modifying all the